Problem
Research questions and friction points this paper is trying to address.
Bayesian structural equation modelling
MCMC
computational efficiency
model refinement
psychometric practice
Implementation and Workflows for INLA-Based Approximate Bayesian Structural Equation Modelling
🤖 AI Summary
This study addresses the computational inefficiency of traditional Markov chain Monte Carlo (MCMC) methods in Bayesian structural equation modeling (SEM), which hinders rapid iterative modeling and diagnostics in psychometrics. The authors introduce, for the first time, a systematic application of integrated nested Laplace approximation (INLA) to complex Bayesian SEMs, implementing it in the R package INLAvaan to enable fast and accurate approximate inference. The proposed approach accommodates high-dimensional parameter models, multilevel mediation analyses, and fully informative missing data handling. In challenging scenarios such as a bifactor circumplex model with 256 parameters, it delivers calibrated posterior summaries within seconds—accelerating computation by several orders of magnitude compared to conventional MCMC while eliminating the need for convergence diagnostics—thereby substantially enhancing both modeling efficiency and practical applicability.
📝 Abstract
Bayesian structural equation modelling (BSEM) offers many advantages such as principled uncertainty quantification, small-sample regularisation, and flexible model specification. However, the Markov chain Monte Carlo (MCMC) methods on which it relies are computationally prohibitive for the iterative cycle of specification, criticism, and refinement that careful psychometric practice demands. We present INLAvaan, an R package for fast, approximate Bayesian SEM built around the Integrated Nested Laplace Approximation (INLA) framework for structural equation models developed by Jamil & Rue (2026, arXiv:2603.25690 [stat.ME]). This paper serves as a companion manuscript that describes the architectural decisions and computational strategies underlying the package. Two substantive applications -- a 256-parameter bifactor circumplex model and a multilevel mediation model with full-information missing-data handling -- demonstrate the approach on specifications where MCMC would require hours of run time and careful convergence work. In constrast, INLAvaan delivers calibrated posterior summaries in seconds.
Innovation
Methods, ideas, or system contributions that make the work stand out.
INLA
Bayesian structural equation modelling
approximate inference
computational efficiency
R package
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